A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2# and the angle between sides B and C is #pi/6#. If side B has a length of 1, what is the area of the triangle?

2 Answers
Binayaka C.
Apr 8, 2016

Areaof the triangle is #0.29# units

Explanation:

This is a right angled triangle.The angle opposite to the side A #/_A=180/6=30^0;/_C=180/2=90^0;/_B=180-(90+30)=60^0#Using sine law we get#B/sinB=A/sinA or A=1.(sin30/sin60)=1/sqrt3#.So Areaof the triangle #= 1/2*base(B)*height(A)=1/2*1*1/sqrt3=0.29#units[Ans]

Alan P.
Apr 8, 2016

Area #=1/(2sqrt(3))~~0.29#

Explanation:

Using the standard trigonometric triangle for #pi/6# and then scaling it to match the given description:
enter image source here

The Area is #1/2AB# (standard formula for a triangle).
#color(white)("XX")=1/2*1*1/sqrt(3) = 1/(2sqrt(3))#

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